Finding large 3-free sets I: The small n case |
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Authors: | William Gasarch James Glenn Clyde P. Kruskal |
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Affiliation: | 1. University of Maryland at College Park, Department of Computer Science, College Park, MD 20742, USA;2. Loyola College in Maryland, Department of Computer Science, 4501 N. Charles St, Baltimore, MD 21210, USA |
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Abstract: | There has been much work on the following question: given n, how large can a subset of be that has no arithmetic progressions of length 3. We call such sets 3-free. Most of the work has been asymptotic. In this paper we sketch applications of large 3-free sets, present techniques to find large 3-free sets of for , and give empirical results obtained by coding up those techniques. In the sequel we survey the known techniques for finding large 3-free sets of for large n, discuss variants of them, and give empirical results obtained by coding up those techniques and variants. |
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